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04042014, 04:44 PM  #1 
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on the (in)accuracy of frame counting method for serve speed calculation
A disclaimer:
I have considered for a long time whether to raise any flag since we all like to use that method to have fun with estimating the serve speed. But these days I see iphone/android/pc apps using that very formula, claiming accuracy. Even charging money for those apps without giving proper credit or even mention to maverick1. Or people now challenging others to bets, claiming that the results given by that formula shows they serve 100mph+. I have a camera recording with 420fps and used my own serve to do the calculations. And that's where the doubts came. Simply stating my servers came up to be too fast. As in, while I have a decent game there's no way I can serve as fast as the calculator shows. So I started digging deeper. I think there are few issues with the calculator (but again, by no means I'm dissing it). The calculation starts with the assumption that the only force acting on the ball is the horizontal force of the air drag. that is a pretty good assumption. But it also implies that:
Given that it seems that the model needs to be a bit more complicated. One that takes into account the fact that the serve is not hit perfectly horizontal  that way it will make sense that the time to bounce will vary between serves. Unfortunately such model will require solving a pair (or a triple if you want to make it really generic and consider side spin too) of differential equations. Now, these days we have mathematica or matlab and given the right model and initial conditions it will solve it for us without much difficulties. (I have actually created such mathematica model if one is interested. ) Anyway, the point is, use it with a grain of salt. If the numbers look too good  they probably are...... 
04042014, 04:46 PM  #2 
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Does your 420 FPS camera actually record exactly at 420?
Seems humidity, temperature, battery level, kind of battery all make a difference, just to add to the variables you listed. 
04042014, 05:50 PM  #3 
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You make a good point about the time to bounce varying based on the angleI think that's going to result in kick serves being estimated as slower than flat serves with the same initial mph.
I'm not so sure that the fact that "fall due to gravity" is sometimes given as 4 feet means that the model is wrong seems like that's just saying how much of the ball's downward motion over the course of its flight to the bounce point can be attributed to gravity (as opposed to serving angle and topspin, which also contribute). The calculator is saying that a ball hit horizontally would have fallen X distance due to gravity by the time it reached the airspace over the bounce point. Right? Also, can you explain a little more why the assumption of a horizontal serve would result in an overly generous estimate of initial speed? Not casting doubt, I just am not following it. Last edited by Avles : 04042014 at 05:52 PM. 
04042014, 06:33 PM  #4  
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Quote:
If we know how much a ball slows from one side to the other in general, which seems plenty consistent for our purposes, how can it be that hard to figure a simple estimate based on distance/time? Every method we have will have some error, but this should be close enough for discussion and comparison between players, right?
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04042014, 06:50 PM  #5  
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04042014, 06:53 PM  #6 
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Jmnk, one problem with your very intricate post. The app is accurate. If you take a video of a serve from a pro match clocked on a radar gun, the app will give you the same speed as the radar gun within a couple mph.
Last edited by Topspin Shot : 04042014 at 07:22 PM. 
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04042014, 07:12 PM  #7 
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jmnk,
The physicist in me wants to agree with you that a more realistic physics model would get us better results. But we don't really want to use a model that's going to require us to use matlab (or at least I don't). If people are +or a few mph as compared to radar results, that's good enough for me. 
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04042014, 08:18 PM  #8  
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It is accurate. There is proof out there. Alves if I remember right tried the frame count method with Drakulie's serve and got pretty much the same result as the radar. 

04042014, 08:39 PM  #9  
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I'd still be interested in hearing a little more about jmnk's objections, just to have a sense of what kinds of errors he thinks are actually occurring. 

04042014, 08:43 PM  #10 
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I'm sure there are plenty of tiny errors, but just expect they don't add up to much.
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04042014, 08:50 PM  #11 
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Could be. I think the biggest issues would be
1. Figuring out distance from racquet to bounce. 2. Whether to add a fraction of a frame with 30 fps video 3. Spinny arcing serves vs. flat serves But if jmnk thinks there's something in the model which is causing it to overstate serve speed I'd like to see an example or a more explicit explanation of how that would happen. 
04042014, 09:18 PM  #12 
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Just to clarify. I'm not affiliated with any iPhone/android app, nor with any radar manufacturer. Just so we get that out of the way.

04042014, 09:34 PM  #13  
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1.assume horizontal hit with no spin. 2.use the formula to calculate the the initial speed 3.since the video gives us the time till bounce  it also calculates, using the very same formula, what was the height the ball was struck from. 4. that's where the discrepancy arises. Because the time from video is way less than it would have been for a freefalling ball. As such, the formula gives you 'distance due to gravity' which is way less than it actually was (for default numbers on the web site, the ball was struck from height about 8.5 feet, but the formula says the fall due to gravity is only 4.29feet.)[/quote] this is not as easy to estimate. I'm comfortable saying that the model is not accurate, I'm less comfortable estimating what the error is. The thing to consider is that a minuscule change in any values entered: height, distance, time, angle of impact, spin, etc has tremendous effect on the calculated result. In other words, given the same time to bounce, and the distance to bounce, I can modify angle and spin of the serve such, that the initial speed will vary greatly (and obviously the serve is still good, in and over the net). It is just a very complex physics model. 

04042014, 09:41 PM  #14  
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04042014, 09:43 PM  #15 
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ok, if you think so, fine with me. It is possible that for SOME serves the numbers happen to be correct. But it is a coincidence.

04042014, 09:45 PM  #16  
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04042014, 09:47 PM  #17  
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04042014, 09:54 PM  #18  
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By anyway, my issue is not with how accurately you can measure the time and distance. I'm trying to point out that even if you measure those very accurately, the formula does not provide an accurate result. 

04042014, 09:58 PM  #19  
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And you do need to measure the time, because the time it takes for the ball to reach the ground depends on how fast the serve is going, as well as on gravity. This is because the serve is not perfectly horizontal. The serve is hit downwards. So serve speed (along with spin) will affect the amount of time it takes to reach the ground. Quote:
What "fall due to gravity" means here is that in .52 seconds a tennis ball in free fall will fall 4.29 feet. This does not imply or assume that the serve being measured was struck from a height of 4.29 feet, because (as I said above) gravity is not the only influence on the time it takes for a serve to reach the ground. Serve trajectory (and hence serve speed) will also play a role. Again, I do not see how the model is assuming that the serve is hit perfectly horizontally. It does seem to assume that the serve travels in a straight line, rather than an arc. But that doesn't mean it's assuming a horizontal serve. Quote:
Last edited by Avles : 04042014 at 10:00 PM. 

04042014, 10:35 PM  #20  
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The fact that the web page suggests you should some distance due to vertical component is just another error in the model. In fact, in this formula, the ONLY distance you should be adding in in pure horizontal direction. Quote:
Quote:
The more generic formula, that takes into account angle of the hit and the spin, is a set of three second order differential equations that cannot be solved analytically. but MATHEMATICA/MATLAB/etc can solve it numerically fairly easily (well, once you set up the equations, which is not trivial). Quote:
But I really like your thinking. Last edited by jmnk : 04042014 at 10:37 PM. 


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